NCSC-23

TO:

FROM:

COPIES TO: Reactor Committee

SUBJECT: Effect of Pb and Bismuth in Thermal Column.

Information was received from

ference

of lead and bismuth gamma shielding. The shield thickness used there is

8"; our calculations had indicated that 4" of Pb was adequate, for which it

had been thought that the neutron attenuation was not serious.

As a check on the

for an 8" spherical shell, as sketched below.

Analysis: the flux equations for the carbon and shield are

where K takes on the value Kc in carbon, Ks in the shield

In the three regions, solutions are assumed

Where the thermal column is assumed to be infinite in extent for calculation

purposes.

Boundary conditions are taken as follows:

[phi]I = 1 at the surface of the core. Normalization to

any known value can be made later.

A comparison between the coefficients E for lead and bismuth serves to

termine

the same in the two cases.

By the application of standard, methods of solution (

including calculation of the K's (reciprocals of the thermal neutron diffusion

lengths) and the [lambda]'s (transport mean free paths), the coefficient E is

computed.

The general solution is:

where =

, and

The constants used were:

Kc = 0.020 cm-1 ; | [lambda]c = 2.72 cm | r1 = 66 cm |

Kpb = 0.085 cm-1 ; | [lambda]Pb = 2.33 cm | r2 = 86.3 cm |

KBi = 0.0187 cm-1; | [lambda]Bi = 3.85 cm |

1, (which is expected because the diffusion lengths for C and Bi are about

the same). Thus the flux with a lead shield is about 1/5 that with a bismuth

shield. No account is taken of impurities in either case. A separate

calculation with a 4" lead shield leads to a factor of 1/3, which would not

be too serious a drop. The problem thus rests on the necessary shield

thickness for protection against gammas.